/// <summary>
/// Prints singular values and condition number.
/// </summary>
public static void Condition(SparseMatrix A, ArpackResult result)
{
if (!EnsureSuccess(result))
{
return;
}
int m = A.RowCount;
int n = A.ColumnCount;
int nconv = result.ConvergedEigenValues;
Console.WriteLine();
Console.WriteLine("Testing ARPACK++ SVD");
Console.WriteLine("Obtaining singular values by solving (A'*A)*v = sigma*v");
Console.WriteLine();
Console.WriteLine("Dimension of the system : " + n);
Console.WriteLine("Number of 'requested' singular values: " + result.Count);
Console.WriteLine("Number of 'converged' singular values: " + nconv);
Console.WriteLine("Number of Arnoldi vectors generated : " + result.ArnoldiCount);
Console.WriteLine("Number of iterations taken : " + result.IterationsTaken);
Console.WriteLine();
var svals = result.EigenValuesReal();
// Calculating singular values.
Console.WriteLine("Singular values of both end:");
for (int i = 0; i < nconv; i++)
{
svals[i] = Math.Sqrt(svals[i]);
Console.WriteLine(" sigma[" + (i + 1) + "]: " + svals[i]);
}
Console.WriteLine();
Console.WriteLine(" Condition number of A : " + (svals[nconv - 1] / svals[0]));
Console.WriteLine();
}
/// <summary>
/// Prints singular values and vectors.
/// </summary>
public static void SVD(SparseMatrix A, ArpackResult result)
{
if (!EnsureSuccess(result))
{
return;
}
int m = A.RowCount;
int n = A.ColumnCount;
int nconv = result.ConvergedEigenValues;
Console.WriteLine();
Console.WriteLine("Testing ARPACK++ SVD");
Console.WriteLine("Compute partial SVD: A = U*S*V'");
Console.WriteLine();
Console.WriteLine("Dimension of the system : " + n);
Console.WriteLine("Number of 'requested' singular values: " + result.Count);
Console.WriteLine("Number of 'converged' singular values: " + nconv);
Console.WriteLine("Number of Arnoldi vectors generated : " + result.ArnoldiCount);
Console.WriteLine("Number of iterations taken : " + result.IterationsTaken);
Console.WriteLine();
var svals = result.EigenValuesReal();
var svecs = result.EigenVectorsReal();
int nAx = (n > m) ? n : m;
// Printing singular values.
Console.WriteLine("Singular values:");
for (int i = 0; i < nconv; i++)
{
Console.WriteLine(" sigma[" + (i + 1) + "]: " + svals[i]);
}
Console.WriteLine();
if (svecs != null)
{
var temp = new double[m + n];
var v = new double[n];
var u = new double[m];
var r = new double[nconv]; // residuals
var s = new double[nconv]; // residuals (transposed system)
for (int i = 0; i < nconv; i++)
{
var sigma = svals[i];
svecs.Column(i, temp);
// Compute A*v - sigma*u
Array.Copy(temp, m, v, 0, n);
Array.Copy(temp, 0, u, 0, m);
A.Multiply(1.0, v, -sigma, u);
r[i] = Vector.Norm(u) / Math.Abs(sigma);
// Compute A'*u - sigma*v
Array.Copy(temp, m, v, 0, n);
Array.Copy(temp, 0, u, 0, m);
A.TransposeMultiply(1.0, u, -sigma, v);
s[i] = Vector.Norm(v) / Math.Abs(sigma);
}
// Printing the residual norm || A*v - sigma*u ||
// for the nconv accurately computed vectors u and v.
for (int i = 0; i < nconv; i++)
{
Console.WriteLine("||A*v(" + (i + 1) + ") - sigma(" + (i + 1) + ")*u(" + (i + 1) + ")||: " + r[i]);
}
Console.WriteLine();
// Printing the residual norm || A'*u - sigma*v ||
// for the nconv accurately computed vectors u and v.
for (int i = 0; i < nconv; i++)
{
Console.WriteLine("||A'*u(" + (i + 1) + ") - sigma(" + (i + 1) + ")*v(" + (i + 1) + ")||: " + s[i]);
}
Console.WriteLine();
}
}
/// <summary>
/// Prints eigenvalues and eigenvectors of symmetric generalized eigen-problems.
/// </summary>
public static void Symmetric(SparseMatrix A, SparseMatrix B, ArpackResult result, ShiftMode mode)
{
if (!EnsureSuccess(result))
{
return;
}
int n = A.RowCount;
int nconv = result.ConvergedEigenValues;
Console.WriteLine();
Console.WriteLine("Testing ARPACK++ class ARluSymGenEig");
Console.WriteLine("Real symmetric generalized eigenvalue problem: A*x - lambda*B*x");
Console.WriteLine();
switch (mode)
{
case ShiftMode.None:
Console.WriteLine("Regular mode");
break;
case ShiftMode.Regular:
Console.WriteLine("Shift and invert mode");
break;
case ShiftMode.Buckling:
Console.WriteLine("Buckling mode");
break;
case ShiftMode.Cayley:
Console.WriteLine("Cayley mode");
break;
}
Console.WriteLine();
Console.WriteLine("Dimension of the system : " + n);
Console.WriteLine("Number of 'requested' eigenvalues : " + result.Count);
Console.WriteLine("Number of 'converged' eigenvalues : " + nconv);
Console.WriteLine("Number of Arnoldi vectors generated: " + result.ArnoldiCount);
Console.WriteLine("Number of iterations taken : " + result.IterationsTaken);
Console.WriteLine();
var evals = result.EigenValuesReal();
var evecs = result.EigenVectorsReal();
// Printing eigenvalues.
Console.WriteLine("Eigenvalues:");
for (int i = 0; i < nconv; i++)
{
Console.WriteLine(" lambda[" + (i + 1) + "]: " + evals[i]);
}
Console.WriteLine();
if (evecs != null)
{
Symmetrize(ref A);
Symmetrize(ref B);
// Printing the residual norm || A*x - lambda*B*x ||
// for the nconv accurately computed eigenvectors.
var x = new double[n];
var y = new double[n];
var r = new double[nconv]; // residuals
for (int i = 0; i < nconv; i++)
{
var lambda = evals[i];
evecs.Column(i, x);
Vector.Copy(x, y);
// y = B*x
B.Multiply(x, y);
// y = A*x - lambda*B*x
A.Multiply(1.0, x, -lambda, y);
r[i] = Vector.Norm(y) / Math.Abs(lambda);
}
for (int i = 0; i < nconv; i++)
{
Console.WriteLine("||A*x(" + i + ") - lambda(" + i + ")*B*x(" + i + ")||: " + r[i]);
}
Console.WriteLine();
}
}